text: vectors can be added to other vectors according to vector algebra a euclidean vector is frequently represented by a line segment with a definite direction or graphically as an arrow connecting an initial point a with a terminal point b and denoted by formula 1 a vector is what is needed to carry the point a to the point b the latin word vector means carrier it was first used by 18th century astronomers investigating planetary revolution around the sun the magnitude of the vector is the distance between the two points and the direction refers to the direction of displacement from a to b many algebraic operations on real numbers such as addition subtraction multiplication and negation have close analogues for vectors operations which obey the familiar algebraic laws of commutativity associativity and distributivity these operations and associated laws qualify euclidean vectors as an example of the more generalized concept of vectors defined simply as elements of a vector space vectors play an important role in physics the velocity and acceleration of a moving object and the forces acting on it can all be described with vectors many other physical quantities can be usefully thought of as vectors although